Question

A conservation organization releases 120 animals of endangered species into a game preserve. The organization believes that the growth of the herd will follow the logistic curve p(t)= 1200/1+9e^ -0.156^t

Answer 1

Given

`P(t)=(1200)/(1+9e^(-0.156t))`

Find

Population after 5 months.

when will population reach 500.

Step-by-step explanation

We have given

`P(t)=(1200)/(1+9e^(-0.156t))`

so population after 5 months.

that is t =5

`\begin{gathered} P(5)=(1200)/(1+9e^(-0.156(5))) \\ \\ P(5)=(1,200)/(1+9e^(-0.78)) \\ \\ P(5)=(1,200)/(1+9*0.458406) \\ \\ P(5)=(1,200)/(5.125654) \\ \\ P(5)=234.116466 \end{gathered}`

Population reach 500

`\begin{gathered} 500=(1200)/(1+9e^(-0.156t)) \\ 1+9e^(-0.156t)=2.4 \\ 9e^(-0.156t)=1.4 \\ t=(\ln((1.4)/(9)))/(-0.156) \\ t=(\ln(0.156))/(-0.156) \\ t=11.90 \end{gathered}`

t = 11.90 months

Final Answer

a) P(5) = 234

b) t = 11.90 months